Your body temperature is typically 37 degrees (Celsius, because this is science). So normally it's cooler around you than inside of you.

If you want to reduce your body temperature, you need to find some way to transfer some of your heat to the outside world. Moving fluids are one of the best ways to transfer heat. You can feel this for yourself if you fill a glass with ice water and let it sit there and then take another glass of ice water and swirl it around. The one you're moving will cool much faster.

Same thing here. More warm blood flowing near the surface of your body, which is exposed to cooler temperatures, means your body temperature is lowered. All that blood will be cooled by being close to the surface of your body, and then it will flow back to your heart through the core of your body.

If you want to conserve heat on the other hand, you restrict blood flow to the surface of your body.

Incidentally, this is why alcohol makes you feel warmer but reduces your body temperature. It opens your capillaries, causing this cooling effect. But having all that warm blood on the surface of your skin makes you feel warmer.

One more extra note: You may wonder why this would matter since your body is going to be exposed to the outside temperature regardless how much warm blood is near the surface of your body. The answer is that the speed at which heat is transferred depends on temperature differential. If you put an ice cube in boiling water, its temperature will increase much faster than an ice cube placed in very cold water. So increasing the temperature differential between your skin and the outside world will make your body temperature change faster.

One final note: I am not a scientist, just someone who reads a fair amount about things like this. There is a chance I made a mistake somewhere!